A new, improved CNC machining center is now available, and experimental data show that it is more accurate than the old machine. It is able to drill the holes such that the distance between the holes is normally distributed with mean 4 cm and standard deviation 0.1 mm. The old CNC center produces brackets where the distance between the holes is normally distributed with mean 4 cm and standard deviation 1.0 mm. The covariance between the distances between the holes drilled on the old and new machine is zero. You want to make sure that for 98% of all the manufactured brackets, the distance between the holes is smaller than 4.03 cm. Required:
How much of the production [%] needs to be at least directed to the new CNC center to achieve this (if you have one new and one old machining center)?